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Simplifying 120 = 0.5s2 + 1.1s Reorder the terms: 120 = 1.1s + 0.5s2 Solving 120 = 1.1s + 0.5s2 Solving for variable 's'. Reorder the terms: 120 + -1.1s + -0.5s2 = 1.1s + -1.1s + 0.5s2 + -0.5s2 Combine like terms: 1.1s + -1.1s = 0.0 120 + -1.1s + -0.5s2 = 0.0 + 0.5s2 + -0.5s2 120 + -1.1s + -0.5s2 = 0.5s2 + -0.5s2 Combine like terms: 0.5s2 + -0.5s2 = 0.0 120 + -1.1s + -0.5s2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -240 + 2.2s + s2 = 0 Move the constant term to the right: Add '240' to each side of the equation. -240 + 2.2s + 240 + s2 = 0 + 240 Reorder the terms: -240 + 240 + 2.2s + s2 = 0 + 240 Combine like terms: -240 + 240 = 0 0 + 2.2s + s2 = 0 + 240 2.2s + s2 = 0 + 240 Combine like terms: 0 + 240 = 240 2.2s + s2 = 240 The s term is 2.2s. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2s + 1.21 + s2 = 240 + 1.21 Reorder the terms: 1.21 + 2.2s + s2 = 240 + 1.21 Combine like terms: 240 + 1.21 = 241.21 1.21 + 2.2s + s2 = 241.21 Factor a perfect square on the left side: (s + 1.1)(s + 1.1) = 241.21 Calculate the square root of the right side: 15.530936868 Break this problem into two subproblems by setting (s + 1.1) equal to 15.530936868 and -15.530936868.Subproblem 1
s + 1.1 = 15.530936868 Simplifying s + 1.1 = 15.530936868 Reorder the terms: 1.1 + s = 15.530936868 Solving 1.1 + s = 15.530936868 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + s = 15.530936868 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + s = 15.530936868 + -1.1 s = 15.530936868 + -1.1 Combine like terms: 15.530936868 + -1.1 = 14.430936868 s = 14.430936868 Simplifying s = 14.430936868Subproblem 2
s + 1.1 = -15.530936868 Simplifying s + 1.1 = -15.530936868 Reorder the terms: 1.1 + s = -15.530936868 Solving 1.1 + s = -15.530936868 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + s = -15.530936868 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + s = -15.530936868 + -1.1 s = -15.530936868 + -1.1 Combine like terms: -15.530936868 + -1.1 = -16.630936868 s = -16.630936868 Simplifying s = -16.630936868Solution
The solution to the problem is based on the solutions from the subproblems. s = {14.430936868, -16.630936868}
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